Aircraft: A300
Phase of flight: Climb
Anomaly: Aircraft Equipment Problem Critical; Inflight Event / Encounter Weather / Turbulence

Departed Runway XXR; light winds from the south; approximately 8 SM; -RA; 050 OVC; 29.93. Due to storms along extended centerline; all flights departing XXR were being turned to heading 080 until clear of storms south and west of the airport. We headed east approximately 15 minutes before Center provided new route: direct and enroute waypoint; then as filed. Center then suggested right turn direct to the enroute waypoint. After we turned; we could see a red cell on weather radar near our route of flight. We were climbing through approximately 13;000 FT. I requested autopilot Number 2. At this time we went IMC; no precipitation was occurring. Approximately 80 NM from red cell; request 15 degrees to the left and remained greater than 20 NM from edge of cell. We continued our climb to FL300. At FL300 we were near the top of the clouds as we could occasionally see patches of blue sky (did not know bottoms; but assumed they were low as we had entered the weather at approximately 13;000 FT). Winds at altitude were out of the northwest at 9 KTS; negative turbulence. Since we had entered IMC; our radio contact with Center continuously deteriorated to the point of being unusable. By the time we reached FL300; another air carrier was passing radio calls between Center and us. We assumed it was either due to interference in the clouds or a problem with Center as we had no issues communicating with the other aircraft. All of our anti-ice systems were operating. At approximately the 30 minute point in the flight; I notice that approximately 25% of my windshield had frosted over and a piece of ice had formed under the windshield wiper arm near the pivot point. One could see ice crystals impacting the nose and windscreen. Soon thereafter; we received an ECAM master caution: Pitot Heat/Captain Pitot Heat Fault. I could see Captain's altimeter climbing and the throttles automatically advanced. All of my flight indications and engine readings were normal. I disconnected auto-throttles (A/T) to prevent over-speeding. This was immediately followed by ECAM IAS Discrepancy; an ADC fault; auto fuel feed fault; and an altitude warning horn. The Captain stated that my data was correct. I was to continue to follow my instruments and she switched her instruments to my side. After the switch; her flight director commanded a slight left turn (3-5 degrees) while mine showed straight and level. Her flight director was ignored. I re-engaged the A/T; but they advanced in contra indication to my flight instruments and our flight conditions and were subsequently disengaged again. Captain announced to the relaying aircraft that we needed left turn for weather and they coordinated as we attempted to get VMC. The heading bug was moved approximately 20 degrees to the left. Aircraft began to turn left when Yaw Damper Number 1 kicked off. When aircraft switched to Yaw Damper Number 2; the nose moved right approximately 3 degrees during the left hand turn. I disconnected A/P and maintained a 15 degree turn. When the yaw damper kicked off it felt as if someone had kicked a rudder pedal. After rolling out of the turn; A/P and yaw damper were reengaged. EMER CANCEL was used repetitively to silence the altitude warning horn. Captain started to run ECAM which was made difficult as the pages seemed to appear and disappear quickly. Apparently higher priority faults would occur then disappear rapidly. The Pitot Heat Fault ECAM was completed. Fault lights initially appeared on Trim Tank pumps; then they went out. System auto switched to Auto Feed Fwd and remained there for the remainder of the flight. We requested and received a descent of perhaps 6;000 FT to FL240 which took us clear of the weather (bottom approximately FL270). We had been in a deck that extended for many miles. Captain initiated a search for ADC1 circuit breaker as directed in one of the ECAM procedures; but the search was abandoned due to higher priorities.Captain requested 'bat phone' to call company. In order to facilitate the operation (phone on right hand side of cockpit); we switched roles and Captain became flying pilot and talked to Center; I worked with Dispatch to discuss issue and backed up the Captain concerning aircraft control. We did not switch back for the remainder of the flight. Radio contact with Center returned to normal at approximately this time. The situation was stable except for nearly continuous altitude warning horn that required continuous and repeated EMER CANCEL. We continued southbound on vectors and eventually exceeding the VHF range thereby losing contact with Flt Control. I asked the Captain to turn back north to return within range. Yaw Damper Number 1 kicked off again and 15 degree angle of bank was utilized for the remainder of the flight to prevent the yaw damper from kicking off. Note: Utilizing RCL (recall) on the ECAM did not return any faults other than PITOT HEAT. I backed up the Captain's completion of this check on the ECAM utilizing my QRH. Dispatch recommended we divert to an airport ahead of us; but due to the continuing questions about flight controls; reduced flight instrument availability; weather over the mountains; we concluded that the appropriate airfield would be an a large airport behind us (to return to the departure airport would require penetrating the previously mentioned T storm that had moved east). We chose to remain VMC for the remainder of the flight. A revised release was received and divert initiated. Note: Once we began our descent to FL200; flight directors agreed; Yaw Damper remained engaged; and the altitude warning horn ceased to be triggered. To facilitate routing as well as requiring vectors utilizing 15 degree AOB; we [advised ATC] at this time. We had 57;000 LBS of fuel on board. At no time did we deviate from the AOM; FOM; or assigned altitude and/or heading without Center approval. Configuration; landing; and taxi to parking were normal. Captain did an excellent job managing the radios; checklists; emergency warnings; and CRM. The First Officer [advised] with ATC and then sent an ACARS message to our Dispatcher also letting him know we were heading to a divert airport. We landed without incident where we were met by CFR equipment. They followed us to the ramp and met us in the cockpit after everything was shut down to see if we needed any other assistance. I think that we handled the situation pretty well. We had a lot of issues to deal with all at one time with regards to communications; instrumentation; and weather. I think we used all of our resources to include using other aircraft to communicate. Looking back I do believe we made the right decision to head to [a nearby airport]. The First Officer and I worked well together with regards to CRM. We were each doing our own thing to get the job done for a while which needed to be done that way; but we made sure we were both back on the same page after decisions were made and that we both felt comfortable with the plan. An A300 in a thin cloud layer top at FL300 encountered an area of light icing; then developed VHF communication difficulties; and an Air Data Computer 1 fault accompanied by Yaw Damper; autopilot; autothrottle; airspeed; and altimeter irregularities. They advised ATC of their situation and diverted to a nearby airport.